Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry

Area of Science:

• Quantum Chemistry
• Computational Science
• Quantum Computing

Background:

• Quantum computing promises significant speedups for complex problems.
• Quantum chemistry, particularly ground-state energy estimation, is a key application area.
• The potential for exponential quantum advantage is under intense investigation.

Purpose of the Study:

• To evaluate the evidence for exponential quantum advantage in ground-state energy estimation for general quantum chemistry problems.
• To assess if efficient quantum state preparation on quantum computers correlates with efficient classical heuristic solutions.
• To determine the realistic scope of quantum advantage in computational quantum chemistry.

Main Methods:

• Numerical studies of quantum state preparation.
• Empirical complexity analysis of classical heuristics, including error scaling.
• Investigation across both ab initio and model Hamiltonian settings.

Main Results:

• Evidence for generic exponential quantum advantage in ground-state energy estimation has not been found.
• The efficiency of quantum state preparation does not consistently translate to superior quantum advantage over classical methods.
• Classical heuristics show competitive or superior performance in many tested scenarios.

Conclusions:

• Exponential quantum advantage is not generically available for ground-state energy estimation in quantum chemistry.
• Quantum computers may offer polynomial speedups, but exponential gains are unlikely for broad chemical applications.
• Further research is needed to identify specific problem classes where quantum computers excel.